This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "re_pelagic"     "Hs_ayg"         "Hs_ay"          "p_slope"       
##   [5] "Ts_ayg"         "Bs_ayg"         "Bs_ay"          "Ts_ay"         
##   [9] "Tdnye_ayg"      "Hdnye_ayg"      "Hd_ayg"         "p_pelagic"     
##  [13] "Bdnye_ayg"      "Hdnye_ay"       "Rs_ay"          "Rs_ay_mort"    
##  [17] "Hd_ay"          "pr_slope"       "Rs_ayg"         "Rs_ayg_mort"   
##  [21] "Rdnye_ayg"      "Rdnye_ayg_mort" "Rd_ayg"         "re_rslope"     
##  [25] "re_slope"       "re_dsr"         "Bs_ayu"         "Ts_ayu"        
##  [29] "Hs_ayu"         "pDSR_YE_ay"     "Hb_ay"          "Hp_ay"         
##  [33] "Hd_ayu"         "Tp_ay"          "p_yellow"       "pDSR_YE_ayu"   
##  [37] "Tb_ay"          "beta3_pH"       "beta2_pH"       "Bp_ay"         
##  [41] "Ho_ayg"         "pDSR_YE_ayg"    "Hb_ayg"         "Bb_ay"         
##  [45] "Hp_ayg"         "Ho_ayu"         "mu_beta2_pH"    "pG"            
##  [49] "H_ayu"          "Rs_ayu_mort"    "Rs_ayu"         "Tp_ayg"        
##  [53] "Tb_ayg"         "H_ay"           "Hdnye_ayu"      "pH"            
##  [57] "Bp_ayg"         "Ho_ay"          "Bb_ayg"         "Ry_ayu"        
##  [61] "Ry_ayu_mort"    "re_yellow"      "Ro_ayg"         "Ry_ay"         
##  [65] "Ry_ay_mort"     "Hy_ayu"         "Bdnye_ay"       "Ro_ayu"        
##  [69] "Ro_ay"          "beta1_pH"       "Tdnye_ay"       "re_pH"         
##  [73] "beta0_pH"       "Hy_ay"          "Rp_ayu"         "Rp_ayu_mort"   
##  [77] "Rb_ayu"         "Rb_ayu_mort"    "Rp_ay_mort"     "Rp_ay"         
##  [81] "Rb_ay_mort"     "Rb_ay"          "Rb_ayg"         "Rb_ayg_mort"   
##  [85] "Rp_ayg_mort"    "Rp_ayg"         "By_ayu"         "Hp_ayu"        
##  [89] "Hb_ayu"         "tau_beta4_pH"   "Hy_ayg"         "Ty_ayg"        
##  [93] "By_ayg"         "mu_beta1_pH"    "R_ayg"          "Ty_ayu"        
##  [97] "By_ay"          "Ty_ay"          "H_ayg"          "beta_H"        
## [101] "Bp_ayu"         "Tp_ayu"         "Ry_ayg_mort"    "Ry_ayg"        
## [105] "Tb_ayu"         "Bb_ayu"         "Tdnye_ayu"      "p_dsr"         
## [109] "Bdnye_ayu"      "R_ayu"          "R_ay"           "tau_beta0_pH"  
## [113] "mu_beta0_pH"    "Rdnye_ayu"      "Rdnye_ayu_mort" "Rdnye_ay"      
## [117] "Rdnye_ay_mort"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pelagic 4 2.030753
beta1_pelagic 6 1.911297
beta2_yellow 3 1.581669
beta3_yellow 2 1.429962
beta2_pelagic 7 1.346440
beta1_black 1 1.317487
beta3_black 1 1.286305
beta3_pelagic 3 1.280150
beta0_yellow 4 1.264540
beta0_black 1 1.255247
beta2_pH 15 1.249423
parameter n badRhat_avg
beta4_pelagic 2 1.248739
beta1_yellow 4 1.246545
beta3_pH 11 1.194524
beta1_pH 14 1.156052
beta0_pH 12 1.151256
beta2_black 1 1.139013
beta_H 3 1.138713
tau_beta0_pH 1 1.123835
mu_beta0_pH 1 1.121824
mu_beta0_pelagic 1 1.111458
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta_H 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0
beta_H 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
beta0_pH 0 1 1 0 1 0 0 1 0 1 2 1 1 1 1 1
beta0_pH 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1
beta1_pH 0 1 2 1 2 0 0 1 1 1 1 1 1 1 0 1
beta1_pH 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1
beta2_pH 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
beta3_pH 1 1 0 1 1 0 0 1 0 1 2 1 0 1 1 0
beta3_pH 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0
Bp_ay 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0
Bp_ayg 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0
Bp_ayu 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0
H_ay 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0
H_ayg 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0
H_ayu 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
Hb_ay 0 0 0 0 0 0 0 2 0 0 23 0 0 0 0 0
Hb_ayg 0 0 0 0 0 0 0 2 0 0 21 0 0 0 0 0
Hb_ayu 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0
Hd_ay 0 0 0 0 0 0 0 0 0 0 21 4 0 0 0 19
Hd_ayg 0 0 0 0 0 0 0 0 0 0 21 4 0 0 0 6
Hd_ayu 0 0 0 0 0 0 0 0 0 0 25 0 0 0 0 17
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 21 4 0 0 0 11
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 19 4 0 0 0 3
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0 15
Ho_ay 0 0 0 0 0 0 0 0 0 0 21 1 0 0 0 11
Ho_ayg 0 0 0 0 2 0 0 0 0 0 21 3 0 0 0 3
Ho_ayu 0 0 0 0 0 1 0 0 0 0 20 0 0 0 0 15
Hp_ay 0 0 0 0 0 0 0 2 0 0 24 0 0 0 0 0
Hp_ayg 0 0 0 0 0 0 0 2 0 0 21 0 0 0 0 0
Hp_ayu 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0
Hs_ay 0 0 0 0 0 0 0 0 0 0 3 43 0 0 0 0
Hs_ayg 0 0 0 0 0 0 0 0 0 0 0 42 0 0 0 0
Hs_ayu 0 0 0 0 0 0 0 0 0 0 1 46 0 0 0 1
Hy_ay 0 0 0 0 1 0 0 0 0 0 21 0 0 0 0 9
Hy_ayg 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0
Hy_ayu 0 0 0 0 2 0 0 0 0 0 15 0 0 0 0 6
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0
p_pelagic 0 0 0 0 0 0 0 0 0 0 50 4 0 0 0 50
p_slope 0 0 0 0 0 0 0 0 0 0 0 88 0 0 0 0
p_yellow 0 0 0 0 0 0 0 0 0 0 0 2 0 6 0 0
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
pG 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
pH 2 0 0 0 0 0 0 0 0 0 4 2 0 1 0 1
pr_slope 0 0 0 0 0 0 0 0 0 0 0 89 0 0 0 0
R_ay 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
R_ayg 0 0 0 3 3 0 1 0 0 0 0 0 0 0 0 0
R_ayu 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
Rb_ay 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0
Rb_ay_mort 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0
Rb_ayg 0 0 0 3 2 0 2 0 0 0 3 0 0 0 0 0
Rb_ayg_mort 0 0 0 3 2 0 2 0 0 0 3 0 0 0 0 0
Rb_ayu 1 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0
Rb_ayu_mort 1 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0
Rd_ayg 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
re_pelagic 0 0 0 0 0 0 0 0 0 0 40 0 0 0 1 39
re_pH 0 10 5 8 4 12 0 17 8 16 15 5 7 8 7 6
re_rslope 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0
re_slope 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0
Ro_ay 0 0 0 0 19 12 0 5 1 0 0 1 0 0 0 0
Ro_ayg 2 0 0 1 3 1 0 1 1 0 0 0 0 0 0 1
Ro_ayu 0 0 0 0 20 13 0 5 1 0 0 1 0 0 0 0
Rp_ay 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0
Rp_ay_mort 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0
Rp_ayg 0 0 0 3 2 0 1 0 0 0 3 0 0 0 0 0
Rp_ayg_mort 0 0 0 3 2 0 1 0 0 0 3 0 0 0 0 0
Rp_ayu 1 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0
Rp_ayu_mort 1 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0
Rs_ay 0 0 0 0 0 0 0 0 0 0 0 46 0 0 0 0
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 0 46 0 0 0 0
Rs_ayg 0 0 0 0 0 0 0 0 0 0 0 42 0 0 0 0
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 42 0 0 0 0
Rs_ayu 0 0 0 0 0 0 0 0 0 0 0 43 0 0 0 0
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 43 0 0 0 0
Ry_ay 0 0 0 0 10 1 0 1 2 0 0 0 0 0 0 0
Ry_ay_mort 0 0 0 0 10 1 0 1 2 0 0 0 0 0 0 0
Ry_ayg 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
Ry_ayg_mort 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
Ry_ayu 0 0 0 0 10 1 0 1 2 0 0 0 0 0 0 0
Ry_ayu_mort 0 0 0 0 10 1 0 1 2 0 0 0 0 0 0 0
tau_beta0_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta4_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 0 0 0 0 0 0 0 2 0 0 21 0 0 0 0 0
Tp_ayg 0 0 0 0 0 0 0 2 0 0 21 0 0 0 0 0
Tp_ayu 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0
beta0_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1
beta0_yellow 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0
beta1_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1
beta1_yellow 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0
beta2_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta2_pelagic 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1
beta2_yellow 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta3_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1
beta3_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
mu_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.132 0.072 -0.267 -0.134 0.017
mu_bc_H[2] -0.102 0.044 -0.180 -0.106 -0.012
mu_bc_H[3] -0.431 0.073 -0.567 -0.434 -0.280
mu_bc_H[4] -0.987 0.190 -1.376 -0.983 -0.632
mu_bc_H[5] 0.890 0.941 -0.205 0.692 3.190
mu_bc_H[6] -2.219 0.323 -2.837 -2.225 -1.568
mu_bc_H[7] -0.447 0.106 -0.660 -0.446 -0.243
mu_bc_H[8] 0.232 0.364 -0.376 0.202 1.027
mu_bc_H[9] -0.294 0.133 -0.552 -0.296 -0.024
mu_bc_H[10] -0.108 0.071 -0.239 -0.110 0.039
mu_bc_H[11] -0.123 0.038 -0.202 -0.121 -0.050
mu_bc_H[12] -0.254 0.110 -0.479 -0.249 -0.051
mu_bc_H[13] -0.142 0.080 -0.304 -0.141 0.011
mu_bc_H[14] -0.304 0.098 -0.508 -0.302 -0.121
mu_bc_H[15] -0.342 0.050 -0.438 -0.343 -0.240
mu_bc_H[16] -0.299 0.370 -0.937 -0.325 0.510
mu_bc_R[1] 1.320 0.142 1.043 1.317 1.611
mu_bc_R[2] 1.458 0.093 1.269 1.458 1.638
mu_bc_R[3] 1.396 0.143 1.101 1.398 1.669
mu_bc_R[4] 0.923 0.198 0.500 0.932 1.271
mu_bc_R[5] 1.229 0.462 0.307 1.236 2.115
mu_bc_R[6] -1.576 0.422 -2.425 -1.572 -0.723
mu_bc_R[7] 0.448 0.203 0.037 0.452 0.842
mu_bc_R[8] 0.540 0.191 0.165 0.541 0.912
mu_bc_R[9] 0.342 0.207 -0.111 0.355 0.712
mu_bc_R[10] 1.315 0.171 0.960 1.322 1.622
mu_bc_R[11] 1.045 0.100 0.852 1.046 1.247
mu_bc_R[12] 0.822 0.203 0.402 0.828 1.207
mu_bc_R[13] 1.032 0.103 0.827 1.033 1.231
mu_bc_R[14] 0.898 0.142 0.620 0.902 1.172
mu_bc_R[15] 0.787 0.114 0.566 0.784 1.010
mu_bc_R[16] 1.101 0.127 0.845 1.102 1.347
tau_pH[1] 4.832 1.048 1.215 5.050 5.988
tau_pH[2] 1.961 0.219 1.564 1.952 2.417
tau_pH[3] 2.146 0.218 1.748 2.135 2.590
beta0_pH[1,1] 0.619 0.326 0.147 0.569 1.702
beta0_pH[2,1] 1.443 0.348 1.004 1.394 2.241
beta0_pH[3,1] 1.415 0.270 0.928 1.400 2.028
beta0_pH[4,1] 1.617 0.280 1.025 1.617 2.328
beta0_pH[5,1] -0.742 0.499 -1.450 -0.811 0.984
beta0_pH[6,1] -0.645 0.542 -1.724 -0.646 0.779
beta0_pH[7,1] -0.315 0.566 -1.339 -0.365 0.815
beta0_pH[8,1] -0.601 0.420 -1.247 -0.635 0.706
beta0_pH[9,1] -0.522 0.470 -1.302 -0.557 0.902
beta0_pH[10,1] 0.425 0.333 -0.111 0.395 1.414
beta0_pH[11,1] 0.093 0.639 -0.442 -0.044 2.275
beta0_pH[12,1] 0.525 0.307 0.109 0.490 1.103
beta0_pH[13,1] 0.100 0.363 -0.272 0.040 1.333
beta0_pH[14,1] -0.230 0.362 -0.630 -0.280 0.628
beta0_pH[15,1] 0.045 0.383 -0.419 -0.009 1.193
beta0_pH[16,1] -0.334 0.507 -1.224 -0.332 0.912
beta0_pH[1,2] 2.829 0.160 2.500 2.833 3.129
beta0_pH[2,2] 2.887 0.138 2.609 2.890 3.160
beta0_pH[3,2] 3.129 0.151 2.846 3.127 3.438
beta0_pH[4,2] 2.949 0.134 2.679 2.947 3.209
beta0_pH[5,2] 4.788 1.359 3.017 4.481 8.201
beta0_pH[6,2] 3.117 0.209 2.709 3.113 3.520
beta0_pH[7,2] 1.829 0.200 1.431 1.827 2.219
beta0_pH[8,2] 2.875 0.176 2.523 2.873 3.213
beta0_pH[9,2] 3.440 0.225 3.013 3.435 3.882
beta0_pH[10,2] 3.696 0.213 3.287 3.693 4.112
beta0_pH[11,2] -4.846 0.316 -5.460 -4.841 -4.272
beta0_pH[12,2] -4.809 0.397 -5.603 -4.810 -4.034
beta0_pH[13,2] -4.583 0.392 -5.345 -4.601 -3.759
beta0_pH[14,2] -5.552 0.479 -6.542 -5.540 -4.673
beta0_pH[15,2] -4.306 0.332 -4.928 -4.304 -3.629
beta0_pH[16,2] -4.866 0.397 -5.721 -4.846 -4.099
beta0_pH[1,3] -0.172 0.718 -1.808 -0.079 1.014
beta0_pH[2,3] 2.193 0.164 1.879 2.190 2.515
beta0_pH[3,3] 2.529 0.150 2.232 2.530 2.819
beta0_pH[4,3] 2.964 0.161 2.651 2.963 3.277
beta0_pH[5,3] 2.134 1.316 0.454 1.865 5.450
beta0_pH[6,3] 1.013 0.486 -0.167 1.043 1.862
beta0_pH[7,3] 0.639 0.175 0.299 0.638 0.994
beta0_pH[8,3] 0.309 0.193 -0.070 0.305 0.693
beta0_pH[9,3] -0.621 0.366 -1.433 -0.605 0.016
beta0_pH[10,3] 0.494 0.371 -0.437 0.537 1.093
beta0_pH[11,3] -0.118 0.336 -0.726 -0.130 0.606
beta0_pH[12,3] -0.886 0.351 -1.614 -0.877 -0.248
beta0_pH[13,3] -0.102 0.337 -0.755 -0.095 0.512
beta0_pH[14,3] -0.259 0.264 -0.763 -0.265 0.264
beta0_pH[15,3] -0.762 0.354 -1.484 -0.729 -0.157
beta0_pH[16,3] -0.378 0.285 -0.944 -0.384 0.192
beta1_pH[1,1] 2.949 0.620 1.098 3.035 3.867
beta1_pH[2,1] 2.079 0.377 1.129 2.103 2.686
beta1_pH[3,1] 2.009 0.439 1.064 2.017 2.837
beta1_pH[4,1] 2.310 0.438 1.259 2.302 3.147
beta1_pH[5,1] 2.148 0.605 0.000 2.220 3.006
beta1_pH[6,1] 3.706 1.422 0.000 3.636 6.497
beta1_pH[7,1] 2.278 1.096 0.000 2.332 4.312
beta1_pH[8,1] 4.147 1.457 0.000 4.228 6.836
beta1_pH[9,1] 2.170 0.648 0.000 2.244 3.183
beta1_pH[10,1] 2.077 0.577 0.000 2.160 2.863
beta1_pH[11,1] 3.114 0.567 1.056 3.210 3.706
beta1_pH[12,1] 2.505 0.366 1.783 2.544 2.977
beta1_pH[13,1] 2.857 0.469 1.386 2.929 3.377
beta1_pH[14,1] 3.312 0.467 2.295 3.374 3.831
beta1_pH[15,1] 2.457 0.415 1.296 2.508 3.009
beta1_pH[16,1] 3.862 0.845 2.149 3.818 5.707
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.010 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.015 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.683 0.339 6.041 6.677 7.338
beta1_pH[12,2] 6.473 0.462 5.612 6.462 7.423
beta1_pH[13,2] 6.958 0.427 6.120 6.964 7.799
beta1_pH[14,2] 7.188 0.497 6.281 7.168 8.212
beta1_pH[15,2] 6.783 0.361 6.056 6.781 7.481
beta1_pH[16,2] 7.455 0.434 6.615 7.433 8.335
beta1_pH[1,3] 4.714 1.679 2.179 4.458 8.423
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.755 7.288 0.858 2.793 13.907
beta1_pH[6,3] 2.974 2.552 0.452 2.627 7.859
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.746 0.348 2.085 2.739 3.442
beta1_pH[9,3] 2.738 0.438 1.978 2.711 3.642
beta1_pH[10,3] 2.881 0.442 2.139 2.840 3.945
beta1_pH[11,3] 2.712 0.393 1.911 2.721 3.460
beta1_pH[12,3] 4.132 0.434 3.312 4.127 5.026
beta1_pH[13,3] 1.692 0.361 1.020 1.694 2.381
beta1_pH[14,3] 2.517 0.349 1.850 2.524 3.197
beta1_pH[15,3] 2.052 0.385 1.323 2.031 2.836
beta1_pH[16,3] 1.777 0.317 1.140 1.788 2.395
beta2_pH[1,1] 0.965 1.966 0.271 0.467 9.103
beta2_pH[2,1] 0.900 1.539 0.262 0.551 6.131
beta2_pH[3,1] 0.846 1.201 0.193 0.466 5.009
beta2_pH[4,1] 0.852 1.716 0.221 0.452 6.215
beta2_pH[5,1] 1.407 1.263 -0.067 1.288 4.185
beta2_pH[6,1] 0.171 0.605 -0.088 0.165 0.571
beta2_pH[7,1] 0.069 0.792 0.000 0.000 0.411
beta2_pH[8,1] 0.227 0.683 0.103 0.205 0.797
beta2_pH[9,1] 0.425 0.652 -0.021 0.391 1.244
beta2_pH[10,1] 0.628 0.732 0.022 0.568 1.671
beta2_pH[11,1] 1.022 1.642 0.392 0.776 2.773
beta2_pH[12,1] 1.532 1.690 0.698 1.248 3.721
beta2_pH[13,1] 0.985 1.595 0.429 0.726 3.411
beta2_pH[14,1] 1.043 1.614 0.527 0.808 2.403
beta2_pH[15,1] 1.002 1.497 0.420 0.771 2.444
beta2_pH[16,1] 0.652 1.692 0.176 0.379 2.307
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.018 1.878 -7.141 -1.502 -0.031
beta2_pH[4,2] -1.916 1.775 -6.649 -1.460 -0.025
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.590 4.444 -21.175 -8.531 -3.950
beta2_pH[12,2] -8.218 5.196 -21.694 -7.387 -0.952
beta2_pH[13,2] -8.029 5.060 -20.824 -7.033 -1.789
beta2_pH[14,2] -8.588 4.738 -20.525 -7.576 -2.646
beta2_pH[15,2] -9.423 4.544 -21.113 -8.432 -3.644
beta2_pH[16,2] -9.601 4.473 -21.456 -8.750 -3.900
beta2_pH[1,3] 0.255 0.421 0.101 0.180 0.681
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.264 6.442 -0.207 8.316 24.084
beta2_pH[6,3] 9.337 6.363 0.289 8.301 24.353
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.289 5.719 2.256 9.291 24.354
beta2_pH[9,3] 9.280 6.273 0.571 8.226 23.863
beta2_pH[10,3] 8.819 6.570 0.505 7.883 24.405
beta2_pH[11,3] -2.453 2.207 -9.272 -1.731 -0.642
beta2_pH[12,3] -2.551 2.125 -9.063 -1.887 -0.936
beta2_pH[13,3] -3.094 2.591 -10.465 -2.216 -0.722
beta2_pH[14,3] -3.035 2.463 -10.335 -2.194 -0.905
beta2_pH[15,3] -3.237 2.488 -10.177 -2.362 -0.890
beta2_pH[16,3] -3.265 2.636 -11.008 -2.342 -0.898
beta3_pH[1,1] 35.693 2.185 33.946 35.891 37.984
beta3_pH[2,1] 33.897 1.987 31.632 33.557 39.539
beta3_pH[3,1] 33.683 1.331 31.270 33.662 36.231
beta3_pH[4,1] 33.769 2.185 31.034 33.849 36.860
beta3_pH[5,1] 27.878 2.255 26.003 27.475 33.575
beta3_pH[6,1] 38.088 4.307 27.511 38.150 45.339
beta3_pH[7,1] 31.241 8.131 18.443 30.839 45.262
beta3_pH[8,1] 40.276 3.799 27.019 40.684 45.368
beta3_pH[9,1] 30.835 2.481 26.653 30.743 35.895
beta3_pH[10,1] 32.821 2.231 26.986 32.962 35.484
beta3_pH[11,1] 30.973 2.677 29.441 30.369 42.796
beta3_pH[12,1] 30.259 1.076 29.296 30.149 31.176
beta3_pH[13,1] 33.257 0.748 32.052 33.233 34.694
beta3_pH[14,1] 32.162 0.723 31.147 32.066 34.434
beta3_pH[15,1] 31.358 1.066 29.989 31.262 33.187
beta3_pH[16,1] 32.032 1.132 30.343 31.898 34.349
beta3_pH[1,2] 30.089 8.047 18.540 29.089 44.904
beta3_pH[2,2] 29.903 7.923 18.529 28.978 44.780
beta3_pH[3,2] 30.200 7.940 18.496 29.262 44.882
beta3_pH[4,2] 30.013 8.013 18.485 29.040 44.951
beta3_pH[5,2] 29.827 7.977 18.393 28.735 44.790
beta3_pH[6,2] 29.892 8.023 18.409 28.696 44.988
beta3_pH[7,2] 29.855 7.979 18.437 28.825 44.827
beta3_pH[8,2] 30.034 8.083 18.558 28.875 45.034
beta3_pH[9,2] 30.146 8.122 18.372 29.189 45.166
beta3_pH[10,2] 30.026 7.919 18.495 29.140 44.740
beta3_pH[11,2] 43.401 0.186 43.105 43.382 43.783
beta3_pH[12,2] 43.190 0.198 42.921 43.145 43.700
beta3_pH[13,2] 43.873 0.145 43.492 43.915 44.042
beta3_pH[14,2] 43.299 0.202 43.047 43.246 43.812
beta3_pH[15,2] 43.424 0.195 43.113 43.403 43.815
beta3_pH[16,2] 43.492 0.187 43.160 43.490 43.834
beta3_pH[1,3] 38.999 3.311 32.767 38.791 45.424
beta3_pH[2,3] 30.206 7.961 18.436 29.484 44.845
beta3_pH[3,3] 30.036 7.988 18.502 29.452 44.865
beta3_pH[4,3] 30.297 7.915 18.511 29.542 44.848
beta3_pH[5,3] 36.891 3.894 31.240 36.263 45.175
beta3_pH[6,3] 40.419 3.443 31.895 40.766 45.550
beta3_pH[7,3] 37.915 4.316 31.321 37.648 45.546
beta3_pH[8,3] 41.489 0.242 41.050 41.492 41.910
beta3_pH[9,3] 33.505 0.528 31.947 33.569 34.292
beta3_pH[10,3] 35.851 0.775 33.612 36.023 36.863
beta3_pH[11,3] 41.658 0.795 40.047 41.692 43.108
beta3_pH[12,3] 41.756 0.388 40.982 41.771 42.521
beta3_pH[13,3] 42.711 0.867 41.041 42.731 44.507
beta3_pH[14,3] 41.086 0.558 39.939 41.103 42.110
beta3_pH[15,3] 42.702 0.704 41.227 42.811 43.856
beta3_pH[16,3] 42.902 0.775 41.106 43.013 44.225
beta0_pelagic[1] 2.221 0.131 1.972 2.222 2.477
beta0_pelagic[2] 1.522 0.117 1.300 1.519 1.751
beta0_pelagic[3] -0.075 0.428 -1.135 0.000 0.569
beta0_pelagic[4] -0.263 0.520 -1.421 -0.214 0.614
beta0_pelagic[5] 1.190 0.252 0.659 1.196 1.667
beta0_pelagic[6] 1.470 0.277 0.878 1.489 1.979
beta0_pelagic[7] 1.597 0.210 1.197 1.589 2.053
beta0_pelagic[8] 1.770 0.206 1.393 1.759 2.232
beta0_pelagic[9] 2.480 0.316 1.873 2.479 3.060
beta0_pelagic[10] 2.508 0.217 2.034 2.517 2.924
beta0_pelagic[11] -0.028 0.516 -1.052 -0.038 0.760
beta0_pelagic[12] 1.670 0.142 1.390 1.670 1.944
beta0_pelagic[13] 0.195 0.274 -0.513 0.230 0.624
beta0_pelagic[14] -0.138 0.263 -0.681 -0.126 0.348
beta0_pelagic[15] -0.271 0.127 -0.518 -0.269 -0.012
beta0_pelagic[16] 0.204 0.350 -0.650 0.292 0.658
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.378 0.585 0.503 1.247 2.611
beta1_pelagic[4] 1.626 0.586 0.622 1.578 2.883
beta1_pelagic[5] -0.064 0.306 -0.654 -0.061 0.546
beta1_pelagic[6] -0.108 0.459 -0.869 -0.171 0.776
beta1_pelagic[7] -0.015 0.295 -0.588 -0.014 0.561
beta1_pelagic[8] -0.013 0.285 -0.580 -0.014 0.560
beta1_pelagic[9] 0.201 0.498 -0.786 0.313 0.959
beta1_pelagic[10] 0.049 0.279 -0.502 0.041 0.607
beta1_pelagic[11] 3.830 1.065 2.082 4.156 5.545
beta1_pelagic[12] 2.752 0.296 2.196 2.757 3.341
beta1_pelagic[13] 3.342 0.901 1.919 3.216 5.447
beta1_pelagic[14] 4.561 1.085 2.861 4.455 7.070
beta1_pelagic[15] 2.980 0.246 2.472 2.982 3.448
beta1_pelagic[16] 3.874 1.038 2.653 3.430 6.215
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.720 2.031 0.061 0.233 5.425
beta2_pelagic[4] 0.683 1.837 0.053 0.327 4.658
beta2_pelagic[5] -0.011 0.684 -1.377 -0.013 1.456
beta2_pelagic[6] -0.102 0.677 -1.449 -0.162 1.301
beta2_pelagic[7] 0.003 0.678 -1.404 0.005 1.479
beta2_pelagic[8] -0.009 0.636 -1.395 -0.009 1.290
beta2_pelagic[9] 0.176 0.685 -1.300 0.248 1.529
beta2_pelagic[10] 0.031 0.656 -1.396 0.031 1.388
beta2_pelagic[11] 2.175 4.359 0.115 0.213 15.238
beta2_pelagic[12] 5.816 4.995 0.967 4.195 19.862
beta2_pelagic[13] 0.550 0.928 0.138 0.344 2.325
beta2_pelagic[14] 0.302 0.156 0.158 0.270 0.629
beta2_pelagic[15] 6.187 4.836 1.289 4.779 19.601
beta2_pelagic[16] 4.184 5.453 0.178 1.884 19.231
beta3_pelagic[1] 29.714 7.873 18.446 28.696 44.897
beta3_pelagic[2] 29.525 7.810 18.455 28.423 44.845
beta3_pelagic[3] 29.943 5.339 20.584 29.373 43.808
beta3_pelagic[4] 24.978 4.786 19.125 23.967 40.281
beta3_pelagic[5] 30.002 8.217 18.427 28.649 45.023
beta3_pelagic[6] 31.727 6.689 18.971 31.741 44.061
beta3_pelagic[7] 29.660 7.816 18.459 28.611 44.921
beta3_pelagic[8] 29.602 7.920 18.427 28.494 44.815
beta3_pelagic[9] 31.085 6.091 19.290 31.148 43.373
beta3_pelagic[10] 29.489 8.089 18.389 28.043 44.906
beta3_pelagic[11] 42.257 2.070 37.443 42.958 45.524
beta3_pelagic[12] 43.460 0.278 42.964 43.450 43.979
beta3_pelagic[13] 43.035 1.505 39.909 43.025 45.663
beta3_pelagic[14] 42.563 1.719 38.903 42.641 45.675
beta3_pelagic[15] 43.202 0.245 42.657 43.200 43.688
beta3_pelagic[16] 43.023 0.922 40.612 43.168 44.804
mu_beta0_pelagic[1] 0.771 0.997 -1.436 0.807 2.726
mu_beta0_pelagic[2] 1.810 0.380 1.015 1.819 2.539
mu_beta0_pelagic[3] 0.256 0.505 -0.811 0.282 1.207
tau_beta0_pelagic[1] 0.514 0.534 0.052 0.347 1.993
tau_beta0_pelagic[2] 2.865 3.415 0.280 2.021 9.833
tau_beta0_pelagic[3] 1.447 1.099 0.186 1.178 4.090
beta0_yellow[1] -0.539 0.190 -0.983 -0.520 -0.226
beta0_yellow[2] 0.509 0.150 0.206 0.514 0.791
beta0_yellow[3] -0.324 0.198 -0.771 -0.317 0.035
beta0_yellow[4] 0.827 0.285 0.015 0.872 1.224
beta0_yellow[5] -0.299 0.351 -0.987 -0.303 0.401
beta0_yellow[6] 1.116 0.162 0.802 1.116 1.433
beta0_yellow[7] 0.992 0.162 0.678 0.995 1.304
beta0_yellow[8] 1.011 0.155 0.706 1.013 1.313
beta0_yellow[9] 0.655 0.159 0.344 0.655 0.968
beta0_yellow[10] 0.588 0.142 0.315 0.588 0.865
beta0_yellow[11] -1.808 0.468 -2.696 -1.828 -0.888
beta0_yellow[12] -3.829 0.516 -4.928 -3.785 -2.949
beta0_yellow[13] -3.787 0.501 -4.875 -3.740 -2.946
beta0_yellow[14] -1.901 0.769 -3.050 -2.051 -0.200
beta0_yellow[15] -2.796 0.376 -3.538 -2.791 -2.043
beta0_yellow[16] -2.389 0.462 -3.334 -2.367 -1.514
beta1_yellow[1] 0.776 0.808 0.012 0.655 2.408
beta1_yellow[2] 1.060 0.342 0.597 1.021 1.789
beta1_yellow[3] 0.708 0.262 0.221 0.703 1.193
beta1_yellow[4] 1.318 0.683 0.631 1.147 3.297
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.994 0.554 0.998 1.993 3.163
beta1_yellow[12] 2.614 0.524 1.713 2.567 3.762
beta1_yellow[13] 2.908 0.504 2.069 2.852 4.031
beta1_yellow[14] 2.009 0.681 0.474 2.113 3.146
beta1_yellow[15] 2.045 0.376 1.276 2.048 2.769
beta1_yellow[16] 2.137 0.455 1.267 2.134 3.072
beta2_yellow[1] -3.810 3.139 -11.432 -3.113 -0.087
beta2_yellow[2] -3.748 3.024 -10.690 -2.997 -0.224
beta2_yellow[3] -3.478 2.779 -9.787 -2.738 -0.170
beta2_yellow[4] -3.727 3.271 -10.209 -2.601 -0.106
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.714 2.837 -11.581 -4.110 -0.166
beta2_yellow[12] -5.145 2.707 -11.691 -4.575 -1.455
beta2_yellow[13] -4.895 2.635 -11.486 -4.329 -1.504
beta2_yellow[14] -4.908 2.891 -11.766 -4.339 -0.712
beta2_yellow[15] -4.581 2.810 -11.463 -3.968 -1.073
beta2_yellow[16] -5.205 2.842 -12.270 -4.634 -1.355
beta3_yellow[1] 26.172 7.307 18.315 22.909 44.369
beta3_yellow[2] 29.045 1.741 25.166 28.894 32.676
beta3_yellow[3] 33.123 3.377 25.507 32.887 42.923
beta3_yellow[4] 29.447 3.551 23.322 28.169 36.512
beta3_yellow[5] 29.785 7.989 18.465 28.743 44.959
beta3_yellow[6] 29.966 7.965 18.455 28.873 44.828
beta3_yellow[7] 30.097 7.976 18.545 29.154 45.027
beta3_yellow[8] 29.954 7.851 18.514 28.939 44.867
beta3_yellow[9] 29.860 7.896 18.484 29.118 44.877
beta3_yellow[10] 30.087 7.789 18.600 28.988 44.927
beta3_yellow[11] 45.085 1.164 43.396 45.297 45.966
beta3_yellow[12] 43.302 0.373 42.553 43.290 43.979
beta3_yellow[13] 44.884 0.388 44.015 44.945 45.564
beta3_yellow[14] 43.087 3.328 33.607 44.153 45.826
beta3_yellow[15] 45.092 0.530 44.105 45.053 45.963
beta3_yellow[16] 44.546 0.663 43.391 44.532 45.833
mu_beta0_yellow[1] 0.093 0.571 -1.120 0.096 1.312
mu_beta0_yellow[2] 0.640 0.338 -0.094 0.664 1.265
mu_beta0_yellow[3] -2.351 0.676 -3.355 -2.459 -0.712
tau_beta0_yellow[1] 1.826 2.436 0.090 1.125 7.494
tau_beta0_yellow[2] 3.408 4.066 0.335 2.383 12.654
tau_beta0_yellow[3] 1.169 1.598 0.078 0.715 4.830
beta0_black[1] -0.076 0.160 -0.395 -0.078 0.247
beta0_black[2] 1.911 0.129 1.663 1.909 2.169
beta0_black[3] 1.312 0.132 1.059 1.309 1.579
beta0_black[4] 2.431 0.135 2.168 2.427 2.692
beta0_black[5] 4.666 2.172 1.808 4.200 10.321
beta0_black[6] 4.659 2.004 2.283 4.125 10.002
beta0_black[7] 3.806 1.946 1.520 3.290 8.901
beta0_black[8] 0.955 0.213 0.524 0.950 1.384
beta0_black[9] 2.601 0.230 2.149 2.600 3.058
beta0_black[10] 1.462 0.133 1.202 1.465 1.722
beta0_black[11] 3.487 0.152 3.189 3.489 3.794
beta0_black[12] 4.866 0.175 4.532 4.869 5.204
beta0_black[13] -0.178 0.587 -0.771 -0.108 0.346
beta0_black[14] 2.857 0.156 2.555 2.857 3.168
beta0_black[15] 1.288 0.158 0.984 1.288 1.595
beta0_black[16] 4.272 0.163 3.948 4.271 4.600
beta2_black[1] 7.836 10.084 0.515 3.501 39.854
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.833 1.518 -6.183 -1.366 -0.202
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.740 1.351 39.726 41.952 43.245
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 38.787 2.704 33.734 39.257 40.529
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.261 0.196 -0.646 -0.260 0.123
beta4_black[2] 0.250 0.184 -0.105 0.249 0.609
beta4_black[3] -0.928 0.191 -1.309 -0.925 -0.564
beta4_black[4] 0.424 0.214 0.003 0.426 0.855
beta4_black[5] 0.568 1.295 -1.226 0.330 3.858
beta4_black[6] 0.550 1.281 -1.220 0.326 3.551
beta4_black[7] 0.450 1.188 -1.339 0.282 3.505
beta4_black[8] -0.236 0.315 -0.867 -0.231 0.371
beta4_black[9] 0.835 0.782 -0.258 0.685 2.706
beta4_black[10] 0.043 0.185 -0.323 0.044 0.412
beta4_black[11] -0.696 0.213 -1.125 -0.692 -0.280
beta4_black[12] 0.176 0.322 -0.423 0.165 0.823
beta4_black[13] -1.183 0.223 -1.623 -1.184 -0.763
beta4_black[14] -0.183 0.234 -0.639 -0.188 0.278
beta4_black[15] -0.880 0.215 -1.300 -0.876 -0.462
beta4_black[16] -0.594 0.235 -1.046 -0.596 -0.134
mu_beta0_black[1] 1.294 0.902 -0.638 1.336 3.131
mu_beta0_black[2] 2.737 1.085 0.722 2.615 5.228
mu_beta0_black[3] 2.485 1.007 0.312 2.555 4.406
tau_beta0_black[1] 0.632 0.596 0.058 0.450 2.208
tau_beta0_black[2] 0.434 0.597 0.045 0.238 1.995
tau_beta0_black[3] 0.237 0.161 0.051 0.198 0.646
beta0_dsr[11] -2.908 0.279 -3.458 -2.908 -2.383
beta0_dsr[12] 4.569 0.284 4.004 4.570 5.149
beta0_dsr[13] -1.456 0.563 -3.165 -1.344 -0.765
beta0_dsr[14] -3.732 0.483 -4.629 -3.754 -2.714
beta0_dsr[15] -2.196 0.823 -5.222 -1.996 -1.384
beta0_dsr[16] -3.013 0.370 -3.744 -3.004 -2.292
beta1_dsr[11] 4.846 0.295 4.250 4.848 5.393
beta1_dsr[12] 8.411 20.278 2.323 5.229 24.244
beta1_dsr[13] 3.028 0.730 2.250 2.867 5.376
beta1_dsr[14] 6.393 0.506 5.325 6.410 7.355
beta1_dsr[15] 4.191 2.444 2.801 3.402 13.267
beta1_dsr[16] 5.827 0.384 5.096 5.820 6.591
beta2_dsr[11] -8.072 2.343 -13.438 -7.798 -4.436
beta2_dsr[12] -6.742 2.644 -12.534 -6.566 -2.010
beta2_dsr[13] -5.754 3.017 -11.539 -5.841 -0.243
beta2_dsr[14] -5.727 2.373 -11.215 -5.227 -2.093
beta2_dsr[15] -6.622 3.387 -13.008 -6.928 -0.059
beta2_dsr[16] -7.668 2.343 -13.235 -7.378 -3.981
beta3_dsr[11] 43.490 0.146 43.219 43.487 43.767
beta3_dsr[12] 33.935 0.719 32.052 34.093 34.794
beta3_dsr[13] 43.295 0.484 42.639 43.207 44.555
beta3_dsr[14] 43.353 0.216 43.080 43.297 43.883
beta3_dsr[15] 42.549 2.805 32.756 43.474 43.863
beta3_dsr[16] 43.441 0.154 43.181 43.428 43.758
beta4_dsr[11] 0.588 0.220 0.177 0.584 1.051
beta4_dsr[12] 0.240 0.451 -0.700 0.234 1.151
beta4_dsr[13] -0.171 0.223 -0.613 -0.169 0.256
beta4_dsr[14] 0.152 0.254 -0.353 0.157 0.638
beta4_dsr[15] 0.723 0.222 0.293 0.724 1.155
beta4_dsr[16] 0.156 0.227 -0.281 0.153 0.597
beta0_slope[11] -1.846 0.148 -2.135 -1.847 -1.558
beta0_slope[12] -5.642 1.798 -9.744 -4.646 -4.017
beta0_slope[13] -1.351 0.204 -1.855 -1.331 -1.013
beta0_slope[14] -2.674 0.165 -2.991 -2.672 -2.346
beta0_slope[15] -1.353 0.152 -1.637 -1.352 -1.059
beta0_slope[16] -2.734 0.156 -3.033 -2.734 -2.431
beta1_slope[11] 4.482 0.222 4.051 4.484 4.907
beta1_slope[12] 4.045 0.752 2.659 4.006 5.909
beta1_slope[13] 2.780 0.576 2.189 2.649 4.753
beta1_slope[14] 6.324 0.410 5.557 6.324 7.142
beta1_slope[15] 3.003 0.210 2.599 3.003 3.404
beta1_slope[16] 5.284 0.288 4.741 5.282 5.877
beta2_slope[11] 8.763 2.372 5.168 8.409 14.288
beta2_slope[12] 6.864 2.868 1.421 6.854 12.853
beta2_slope[13] 5.332 3.180 0.308 5.353 11.524
beta2_slope[14] 6.432 2.504 2.400 6.305 11.857
beta2_slope[15] 8.282 2.419 4.431 8.001 14.072
beta2_slope[16] 7.887 2.346 4.320 7.579 13.503
beta3_slope[11] 43.459 0.134 43.217 43.453 43.726
beta3_slope[12] 40.350 4.248 33.925 43.169 43.845
beta3_slope[13] 43.491 0.456 42.925 43.416 44.656
beta3_slope[14] 43.266 0.133 43.093 43.235 43.598
beta3_slope[15] 43.484 0.216 43.187 43.485 43.797
beta3_slope[16] 43.374 0.144 43.149 43.354 43.695
beta4_slope[11] -0.726 0.167 -1.050 -0.723 -0.405
beta4_slope[12] -0.940 0.528 -2.047 -0.910 -0.018
beta4_slope[13] 0.081 0.160 -0.235 0.079 0.401
beta4_slope[14] -0.091 0.197 -0.474 -0.092 0.302
beta4_slope[15] -0.753 0.158 -1.061 -0.749 -0.445
beta4_slope[16] -0.160 0.175 -0.493 -0.163 0.194
sigma_H[1] 0.199 0.054 0.103 0.195 0.315
sigma_H[2] 0.173 0.030 0.119 0.171 0.238
sigma_H[3] 0.198 0.043 0.122 0.195 0.289
sigma_H[4] 0.421 0.078 0.294 0.412 0.598
sigma_H[5] 0.986 0.209 0.612 0.974 1.427
sigma_H[6] 0.436 0.191 0.058 0.433 0.834
sigma_H[7] 0.308 0.062 0.212 0.299 0.455
sigma_H[8] 0.413 0.092 0.266 0.404 0.611
sigma_H[9] 0.527 0.125 0.330 0.511 0.818
sigma_H[10] 0.210 0.045 0.134 0.207 0.304
sigma_H[11] 0.278 0.046 0.200 0.273 0.385
sigma_H[12] 0.435 0.164 0.207 0.413 0.756
sigma_H[13] 0.214 0.038 0.148 0.211 0.295
sigma_H[14] 0.506 0.091 0.346 0.498 0.700
sigma_H[15] 0.245 0.040 0.177 0.242 0.334
sigma_H[16] 0.227 0.045 0.154 0.221 0.326
lambda_H[1] 3.290 4.360 0.154 1.843 14.736
lambda_H[2] 8.482 7.883 0.774 6.152 30.222
lambda_H[3] 6.117 8.623 0.273 3.181 28.790
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.534 8.400 0.033 0.979 24.902
lambda_H[6] 5.615 12.324 0.008 0.459 44.297
lambda_H[7] 0.013 0.009 0.002 0.011 0.036
lambda_H[8] 8.138 10.708 0.003 4.433 37.623
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.290 0.537 0.031 0.190 1.082
lambda_H[11] 0.287 0.445 0.011 0.138 1.302
lambda_H[12] 5.125 7.143 0.189 2.718 24.137
lambda_H[13] 3.488 3.276 0.236 2.634 11.968
lambda_H[14] 3.299 4.151 0.222 2.008 13.841
lambda_H[15] 0.029 0.223 0.003 0.017 0.095
lambda_H[16] 1.061 1.947 0.048 0.509 5.054
mu_lambda_H[1] 4.345 1.860 1.251 4.184 8.476
mu_lambda_H[2] 3.746 1.949 0.552 3.557 7.831
mu_lambda_H[3] 3.524 1.892 0.745 3.226 7.875
sigma_lambda_H[1] 8.574 4.211 2.120 7.939 17.843
sigma_lambda_H[2] 8.195 4.737 1.016 7.605 18.465
sigma_lambda_H[3] 6.261 4.053 0.945 5.348 16.484
beta_H[1,1] 6.923 1.060 4.373 7.077 8.530
beta_H[2,1] 9.870 0.486 8.794 9.891 10.730
beta_H[3,1] 7.990 0.780 6.079 8.112 9.186
beta_H[4,1] 9.156 7.769 -6.902 9.196 24.323
beta_H[5,1] 0.143 2.428 -4.862 0.296 4.496
beta_H[6,1] 2.995 4.041 -6.824 4.289 7.880
beta_H[7,1] 0.763 5.760 -11.138 1.074 11.219
beta_H[8,1] 2.179 7.049 -2.378 1.254 23.975
beta_H[9,1] 13.164 5.748 1.783 13.190 25.015
beta_H[10,1] 7.066 1.684 3.536 7.126 10.332
beta_H[11,1] 5.219 3.511 -2.570 6.051 10.010
beta_H[12,1] 2.619 1.054 0.798 2.536 4.976
beta_H[13,1] 9.019 0.933 7.057 9.095 10.512
beta_H[14,1] 2.226 1.022 0.248 2.222 4.294
beta_H[15,1] -6.126 3.840 -12.872 -6.342 2.057
beta_H[16,1] 3.371 2.464 -0.650 3.063 9.271
beta_H[1,2] 7.909 0.241 7.441 7.914 8.350
beta_H[2,2] 10.026 0.135 9.765 10.026 10.298
beta_H[3,2] 8.960 0.191 8.582 8.956 9.338
beta_H[4,2] 3.582 1.474 0.810 3.533 6.594
beta_H[5,2] 1.946 0.921 0.109 1.953 3.697
beta_H[6,2] 5.728 1.036 3.319 5.879 7.370
beta_H[7,2] 2.603 1.087 0.634 2.553 4.887
beta_H[8,2] 2.808 1.766 -3.863 3.124 4.260
beta_H[9,2] 3.448 1.113 1.313 3.406 5.742
beta_H[10,2] 8.199 0.351 7.469 8.203 8.861
beta_H[11,2] 9.743 0.629 8.834 9.610 11.157
beta_H[12,2] 3.940 0.374 3.234 3.921 4.728
beta_H[13,2] 9.129 0.258 8.678 9.123 9.658
beta_H[14,2] 4.041 0.344 3.368 4.040 4.706
beta_H[15,2] 11.360 0.683 9.957 11.402 12.611
beta_H[16,2] 4.584 0.813 3.069 4.556 6.222
beta_H[1,3] 8.461 0.233 8.053 8.445 8.955
beta_H[2,3] 10.074 0.113 9.856 10.072 10.296
beta_H[3,3] 9.606 0.165 9.291 9.603 9.952
beta_H[4,3] -2.517 0.893 -4.258 -2.533 -0.765
beta_H[5,3] 3.872 0.601 2.635 3.890 5.059
beta_H[6,3] 8.111 1.196 6.401 7.782 10.620
beta_H[7,3] -2.768 0.660 -4.041 -2.763 -1.461
beta_H[8,3] 5.352 0.816 4.672 5.198 8.288
beta_H[9,3] -2.789 0.759 -4.312 -2.771 -1.356
beta_H[10,3] 8.698 0.277 8.167 8.699 9.245
beta_H[11,3] 8.559 0.288 7.918 8.588 9.053
beta_H[12,3] 5.254 0.317 4.496 5.295 5.755
beta_H[13,3] 8.856 0.180 8.487 8.858 9.210
beta_H[14,3] 5.713 0.279 5.077 5.733 6.201
beta_H[15,3] 10.368 0.321 9.744 10.359 11.007
beta_H[16,3] 6.355 0.658 4.928 6.419 7.498
beta_H[1,4] 8.271 0.180 7.884 8.283 8.585
beta_H[2,4] 10.146 0.117 9.896 10.153 10.349
beta_H[3,4] 10.114 0.161 9.755 10.123 10.407
beta_H[4,4] 11.792 0.449 10.900 11.810 12.630
beta_H[5,4] 5.539 0.775 4.275 5.438 7.370
beta_H[6,4] 7.058 0.915 5.057 7.303 8.351
beta_H[7,4] 8.257 0.344 7.578 8.264 8.953
beta_H[8,4] 6.683 0.346 5.626 6.722 7.131
beta_H[9,4] 7.190 0.465 6.263 7.176 8.123
beta_H[10,4] 7.737 0.238 7.292 7.727 8.230
beta_H[11,4] 9.382 0.198 8.982 9.380 9.771
beta_H[12,4] 7.141 0.214 6.732 7.136 7.582
beta_H[13,4] 9.053 0.145 8.765 9.053 9.332
beta_H[14,4] 7.728 0.220 7.301 7.727 8.172
beta_H[15,4] 9.463 0.235 9.004 9.461 9.934
beta_H[16,4] 9.330 0.238 8.902 9.315 9.822
beta_H[1,5] 8.998 0.141 8.710 8.999 9.280
beta_H[2,5] 10.787 0.094 10.604 10.787 10.975
beta_H[3,5] 10.916 0.173 10.598 10.909 11.264
beta_H[4,5] 8.376 0.460 7.503 8.359 9.307
beta_H[5,5] 5.421 0.574 4.066 5.463 6.401
beta_H[6,5] 8.922 0.639 7.951 8.800 10.382
beta_H[7,5] 6.745 0.339 6.078 6.746 7.419
beta_H[8,5] 8.243 0.269 7.866 8.208 8.906
beta_H[9,5] 8.215 0.475 7.276 8.213 9.142
beta_H[10,5] 10.101 0.227 9.631 10.104 10.533
beta_H[11,5] 11.503 0.230 11.056 11.500 11.978
beta_H[12,5] 8.478 0.196 8.099 8.477 8.881
beta_H[13,5] 10.016 0.136 9.755 10.018 10.287
beta_H[14,5] 9.203 0.233 8.775 9.190 9.693
beta_H[15,5] 11.167 0.241 10.687 11.166 11.644
beta_H[16,5] 9.926 0.178 9.562 9.933 10.255
beta_H[1,6] 10.171 0.188 9.850 10.155 10.594
beta_H[2,6] 11.510 0.107 11.298 11.512 11.720
beta_H[3,6] 10.813 0.161 10.472 10.821 11.106
beta_H[4,6] 12.873 0.806 11.224 12.880 14.432
beta_H[5,6] 5.901 0.587 4.789 5.891 7.106
beta_H[6,6] 8.887 0.658 7.158 9.004 9.877
beta_H[7,6] 9.850 0.567 8.692 9.849 10.965
beta_H[8,6] 9.480 0.374 8.623 9.525 9.943
beta_H[9,6] 8.449 0.797 6.857 8.446 10.088
beta_H[10,6] 9.509 0.319 8.837 9.530 10.083
beta_H[11,6] 10.818 0.355 9.990 10.860 11.431
beta_H[12,6] 9.377 0.257 8.899 9.367 9.922
beta_H[13,6] 11.042 0.164 10.745 11.032 11.388
beta_H[14,6] 9.829 0.296 9.225 9.841 10.403
beta_H[15,6] 10.839 0.425 10.011 10.846 11.663
beta_H[16,6] 10.550 0.231 10.057 10.561 10.968
beta_H[1,7] 10.859 0.861 8.721 10.968 12.216
beta_H[2,7] 12.202 0.429 11.313 12.203 13.047
beta_H[3,7] 10.560 0.653 9.078 10.630 11.662
beta_H[4,7] 2.444 4.136 -5.459 2.420 10.911
beta_H[5,7] 6.464 1.820 3.203 6.398 10.773
beta_H[6,7] 9.658 2.395 4.953 9.606 16.024
beta_H[7,7] 10.500 2.896 5.152 10.456 16.502
beta_H[8,7] 11.081 1.508 9.407 10.906 14.459
beta_H[9,7] 4.492 4.110 -3.865 4.430 12.536
beta_H[10,7] 9.863 1.471 7.156 9.764 12.967
beta_H[11,7] 10.997 1.744 7.929 10.864 14.926
beta_H[12,7] 9.963 0.977 7.771 10.045 11.524
beta_H[13,7] 11.627 0.748 9.851 11.725 12.798
beta_H[14,7] 10.379 0.936 8.359 10.451 11.997
beta_H[15,7] 11.962 2.206 7.735 11.969 16.253
beta_H[16,7] 12.216 1.203 10.263 12.052 14.989
beta0_H[1] 8.795 13.541 -20.578 8.875 36.602
beta0_H[2] 10.791 6.389 -2.155 10.744 23.673
beta0_H[3] 9.545 10.023 -12.395 9.817 29.800
beta0_H[4] 4.472 188.735 -379.541 5.661 384.792
beta0_H[5] 4.970 25.403 -42.070 4.310 54.286
beta0_H[6] 8.398 49.811 -101.527 7.815 119.782
beta0_H[7] 3.966 137.881 -263.217 3.836 287.342
beta0_H[8] 5.434 52.988 -23.496 6.521 37.199
beta0_H[9] 4.762 125.512 -244.291 5.479 254.782
beta0_H[10] 8.085 34.041 -59.775 8.219 79.321
beta0_H[11] 10.834 49.105 -96.485 10.424 113.120
beta0_H[12] 6.828 11.259 -14.451 6.686 29.098
beta0_H[13] 9.907 11.442 -11.334 10.064 31.330
beta0_H[14] 7.047 11.589 -16.117 6.900 31.411
beta0_H[15] 11.478 104.280 -194.437 10.533 227.147
beta0_H[16] 7.747 24.967 -42.637 7.881 54.917